🧮 algebra

1. **State the problem:** An engineer drives to his brother's house at 50 mph and it takes 3 hours. We need to find the time it takes to drive back at 60 mph. 2. **Calculate the di

1. **State the problem:** We have a stamping machine that can stamp 40 envelopes in 8 minutes. We want to find how many such machines working simultaneously are needed to stamp 120

1. Muammo: $X$ ning qiymati 9 chiqadi, lekin 12 noto'g'ri natija sifatida berilgan. 2. Bu yerda $X$ ning qiymatini topish uchun tenglama yoki ifoda kerak.

1. **State the problem:** An engineer drives to his brother's house at 50 mph taking 3 hours. We need to find the time it takes to drive back at 60 mph. 2. **Calculate the distance

1. **State the problem:** We have the matrix equation \( \begin{bmatrix} 2 & 1 \\ 3 & 2 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 23 \\ 37 \end{bmatrix}

1. The problem states that \( \frac{AC}{36} = \frac{60}{48} \). 2. To find \( AC \), we can cross-multiply: \( AC \times 48 = 60 \times 36 \).

1. **State the problem:** We need to solve for the principal amount $P$ in the equation $$27660 = P(1 + 6.7\%)^5.$$ 2. **Convert the percentage to decimal:**

1. **State the problem:** Mary has a parcel weighing 10.5 kg and needs to split it into two parcels, each weighing at most 6 kg, to ship to China. The shipping cost depends on the

1. Problem a) Simplify $\sqrt{25a^{2}b^{2}} \times \sqrt[3]{27a^{3}}$. - $\sqrt{25a^{2}b^{2}} = 5ab$ because $\sqrt{25} = 5$, $\sqrt{a^{2}} = a$, and $\sqrt{b^{2}} = b$.

1. The problem is to solve the inequality $x^2 + 5x + 4 \geq 0$. 2. First, factor the quadratic expression: $x^2 + 5x + 4 = (x + 4)(x + 1)$.

1. **Problem statement:** Find the domain and range of the functions: a. $f(x) = 3x^{\frac{4}{5}}$

1. **State the problem:** Solve the quadratic equation $$5x^2 + 25x = 0$$. 2. **Factor the equation:** Factor out the common term $$5x$$:

1. The problem is to solve the equation, but the equation itself is missing from the user's message. 2. Please provide the specific equation you want to solve so I can assist you s

1. Let's start by understanding what a graphical inequality means. When you have an inequality involving a function, such as $y > f(x)$ or $y \leq f(x)$, it represents all the poin

1. Problem: Find the inverse of each function. 2. For function a: $f(x) = 3x - 2$

1. **State the problem:** You manage a 90-unit apartment building. Rent starts at 20000 per unit with full occupancy. For every 1000 increase in rent, one more unit becomes vacant.

1. The problem is to graph the function, but no specific function was provided. 2. To graph a function, we need its explicit formula, for example, $y = x^2$ or $y = \sin(x)$.

1. **State the problem:** You are managing a 90-unit apartment building. The base rent is 20000 per unit with full occupancy. For every 1000 increase in rent, one unit becomes vaca

1. Let's analyze the problem: We want to determine the value of $x$ and check if it could be 36 or 24, given the statement that $x$ is clearly larger than 12. 2. Since $x$ is large

1. نبدأ بكتابة المعادلة المعطاة: $$ س^2 + ص^2 = ك $$ 2. نريد التعبير عن $$ ص^2 $$ بدلالة $$ ك $$ و $$ س^2 $$.

1. The problem is to find the equation of the line passing through the points $(1,2)$ and $(3,8)$. 2. First, calculate the slope $m$ using the formula: